What is (\partial)/(\partial x)(e^{xln(y)}) ?

The answer to (\partial)/(\partial x)(e^{xln(y)}) is y^xln(y)

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(\partial)/(\partial x)(e^{xln(y)})

\frac{\partial}{\partial x} (e^{x l n (y)})

y^{x} ln (y)

Solution steps

\frac{\partial}{\partial x} (e^{x l n (y)})

Simplify

e^{x l n (y)} : y^{x}

= \frac{\partial}{\partial x} (y^{x})

Treat

y

as a constant

Apply the derivative exponent rule:

\frac{d}{d x} (a^{x}) = a^{x} ln (a)

= y^{x} ln (y)

x \to 2 lim (\frac{x}{( x - 2 ) ^{2}})

2 x^{4} - 11 x^{2}

\frac{\partial}{\partial x} (\frac{G ( x , y , r ) x y}{r ^{2}})

f (x) = \frac{x ^{2} - a ^{2}}{x ^{2} + a ^{2}}

\int ln (1 + \frac{1}{x}) d x

What is (\partial)/(\partial x)(e^{xln(y)}) ?
The answer to (\partial)/(\partial x)(e^{xln(y)}) is y^xln(y)